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Developments in the ability to analyse online data of people's names have provided breakthroughs for social research, however, there are several existing challenges. This thesis proposes several novel approaches for identifying hidden properties and text diversity translation of people's names. We start by studying the hidden properties of people's names and found that there are limited existing methods to identify more than one hidden property of people's names at one time. We, therefore, propose a 'Hidden Property Bayes' model that achieves identifying more than one hidden property of people's names in Kanji and Hanzi at one time. In addition, our model performs better than an existing system on name origin identification. We then moved on to text diversity translation and found that translating romanised names to the original language is a challenge. Therefore, we propose two novel models to translate Pinyin names to Hanzi names. These two novel models perform better than 'google translate' on Mandarin name translation. We next investigated gender prediction of people's names and found that limited existing tools can predict and analyse the data in one process. Therefore, we propose a 'Name-Gender' tool that achieves predicting the gender of people's names and also provides a statistical graph directly. In addition, our tool has better performance than an existing system on predicting the genders of people's names in Latin and Hanzi characters. We also provide novel findings of gender analysis in computer science using our 'Name-Gender' tool approaches. Overall, our contributions provide effective novel approaches to support social researchers analysing online data sources of people's names to aid them in understanding real-world events.

Type systems were invented in the early 1900s to provide foundations for Mathematics where types were used to avoid paradoxes. Type systems have then been developed and extended throughout the years to serve different purposes such as efficiency or expressiveness. The λ-calculus is used in programming languages, logic, mathematics, and linguistics. Intersection types are a kind of types used for building semantic models of the λ-calculus and for static analysis of computer programs. The confluence property was used to prove the λ-calculus’ consistency and the uniqueness of normal forms. Confluence is useful to show that logics are sensibly designed, and to make equality decision procedures for use in theorem provers. Some proofs of the λ-calculus’ confluence are based on syntactic concepts (reduction relations and λ-term sets) and some on semantic concepts (type interpretations). Part I of this thesis presents an original syntactic proof that is a simplification of a semantic proof based on a sound type interpretation w.r.t. an intersection type system. Our proof can be seen as bridging some semantic and syntactic proofs. Expansion is an operation on typings (pairs of type environments and result types) in type systems for the λ-calculus. It was introduced to prove that the principal typing property (i.e., that every typable term has a strongest typing) holds in intersection type systems. Expansion variables were introduced to simplify the expansion mechanism. Part II of this thesis presents a complete realisability semantics w.r.t. an intersection type system with infinitely many expansion variables. This represents the first study on semantics of expansion. Providing sound (and complete) realisability semantics allows one to study the algorithmic behaviour of typed λ-terms through their types w.r.t. a type system. We believe such semantics will cast some light on the not yet well understood expansion operation. Intersection types were used in a type error slicer for the SML programming language. Existing compilers for many languages have confusing type error messages. Type error slicing (TES) helps the programmer by isolating the part of a program contributing to a type error (a slice). TES was initially done for a tiny toy language (the λ-calculus with polymorphic let-expressions). Extending TES to a full language is extremely challenging, and for SML we needed a number of innovations. Some issues would be faced for any language, and some are SML-specific but representative of the complexity of language-specific issues likely to be faced for other languages. Part III of this thesis solves both kinds of issues and presents an original, simple, and general constraint system for providing type error slices for ill-typed programs. We believe TES helps demystify language features known to confuse users.

Shape types are a general concept of process types which allows verification of various properties of processes from various calculi. The key property is that shape types “look like processes”, that is, they resemble process structure and content. PolyV, originally designed by Makholm and Wells, is a type system scheme which can be instantiated to a shape type system for many calculi. Every PolyV instantiation has desirable properties including subject reduction, polymorphism, the existence of principal typings, and a type inference algorithm. In the first part of this thesis, we fix and describe inconsistencies found in the original PolyV system, we extend the system to support name restriction, and we provide a detailed proof of the correctness of the system. In the second part, we present a description of the type inference algorithm which we use to constructively prove the existence of principal typings. In the third part, we present various applications of shape types which demonstrate their advantages. Furthermore we prove that shape types can provide the same expressive power as and also strictly superior expressive power than predicates of three quite dissimilar analysis systems from the literature, namely, (1) an implicitly typed π-calculus, (2) an explicitly typed Mobile Ambients, (3) and a flow analysis system for BioAmbients.

There are many proof checking tools that allow capturing mathematical knowledge into formal representation. Those proof systems allow further automatic verifica- tion of the logical correctness of the captured knowledge. However, the process of encoding common mathematical documents in a chosen proof system is still labour- intensive and requires comprehensive knowledge of such system. This makes the use of proof checking tools inaccessible for ordinary mathematicians. This thesis provides a solution for the computerisation of mathematical documents via a num- ber of gradual steps using the MathLang framework. We express the full process of formalisation into the Mizar proof checker. The first levels of such gradual computerisation path have been developing well before the course of this PhD started. The whole project, called MathLang, dates back to 2000 when F. Kamareddine and J.B. Wells started expressing their ideas of novel approach for computerising mathematical texts. They mainly aimed at developing a mathematical framework which is flexible enough to connect existing, in many cases different, approaches of computerisation mathematics, which allows various degrees of formalisation (e.g., partial, full formalisation of chosen parts, or full formalisation of the entire doc- ument), which is compatible with different mathematical foundations (e.g., type theory, set theory, category theory, etc.) and proof systems (e.g., Mizar, Isar, Coq, HOL, Vampire). The first two steps in the gradual formalisation were developed by F. Kamareddine, J.B. Wells and M. Maarek with a small contribution of R. Lamar to the second step. In this thesis we develop the third level of the gradual path, which aims at capturing the rhetorical structure of mathematical documents. We have also integrated further steps of the gradual formalisation, whose final goal is the Mizar system. We present in this thesis a full path of computerisation and formalisation of math- ematical documents into the Mizar proof checker using the MathLang framework. The development of this method was driven by the experience of computerising a number of mathematical documents (covering different authoring styles).

This thesis introduces of a system of tense logic called nominal tense logic (NTL), and several extensions. Its primary aim is to establish that these systems are logically interesting, and can provide useful models of natural language tense, temporal reference, and their interaction. Languages of nominal tense logic are a simple augmentation of Priorean tense logic. They add to the familiar Priorean languages a new sort of atomic symbol, nominals. Like propositional variables, nominals are atomic sentences and may be freely combined with other wffs using the usual connectives. When interpreting these languages we handle the Priorean components standardly, but insist that nominals must be true at one and only one time. We can think of nominals as naming this time. Logically, the change increases the expressive power of tensed languages. There are certain intuitions about the flow of time, such as irreflexivity, that cannot be expressed in Priorean languages; with nominals they can. The effects of this increase in expressive power on the usual model theoretic results for tensed languages discussed, and completeness and decidability results for several temporally interesting classes of frames are given. Various extensions of the basic system are also investigated and similar results are proved. In the final chapter a brief treatment of similarly referential interval based logics is presented. As far as natural language semantics is concerned, the change is an important one. A familiar criticism of Priorean tense logic is that as it lacks any mechanism for temporal reference, it cannot provide realistic models of natural language temporal usage. Natural language tense is at least partly about referring to times, and nowadays the deictic and anaphoric properties of tense are a focus of research. The thesis presents a uniform treatment of certain temporally referring expressions such as indexicals, and simple discourse phenomena.